[Geoqus] Questions about viscoplasticity

[Chris Salomon]

Dear GEOQUS Members,


  I have some questions related to the theory of viscoplasticity.  
Maybe there's someone here who can help me.


  I wrote an UMAT for a (at this moment simple) viscoplastic model.  
But I'm not sure if everything is correct.


  I use the Return Mapping algorithm by Simo and Hughes (1998,  
Computational Inelasticity, Box 3.8 (P. 156) in combination with Box  
3.5 (P. 159)). Therefore it seems as if I can simply replace the  
consistency parameter (lambda) for the plastic regime with its  
counterpart in the viscoplastic regime (p). I.e. I currently use  
Perzyna's model (1966, Fundamental Problems inviscoplasticity, Rec.  
Adv. Appl. Mech. 9) for which I set

  p=1/Viscosity*(f/Yield)^N

  whereas f is the yield-function and Yield the corresponding  
yield-stress. The viscoplastic strain-rate therefore becomes

  de_(vp)=p*df/d(stress).

  Questions:

  1. Can I simply replace the consistency parameter with p and still  
use  the algorithm out of Box 3.5 from Simo and Hughes? (I also want  
to include isotropic and kinematic hardening!)

  2. Is my definition of p correct? Because p now has the units  
1/(Pa*s) but I would expect it to be 1/s.

  3. I want to model subduction zones with this but am not sure if I  
should use an associative or non-associative flow-law. What do you  
think is better? For example Fossum and Brannon (2004, The SANDIA  
GeoMode: Theory and User's Guide) use non-associative flow-laws  
according to the works by Miller and Cheatham (1972, A new yield  
condition and hardening rule for rocks, Int. J. Rock Mech. Min. Sci. 9).


  I would really appreciate it if someone could help me.

  Greetings
  Chris Salomon



  PS. For a review see e.g. Chaboche (2008, A review of some  
plasticity and viscoplasticity constitutive theories, Int. J. Plas. 24).

  PPS. A much simpler version of the Return Mapping Algorithm can be  
found in Zeng et al. (1996, Numerical implementation of constitutive  
integration for rate-dependent elastoplasticity, Comp. Mech. 18).